{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import random"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(x):\n",
    "    return 1/(1+np.exp(-x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "def random_linear(x):\n",
    "    k,b=random.random(),random.random()\n",
    "    print(k,b)\n",
    "    return k*x+b"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "sub_x=np.linspace(-10,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for _ in range(5):\n",
    "    plt.plot(sub_x,random_linear(sigmoid(random_linear(sub_x))))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.3343249276642528 0.24811489325279212\n",
      "0.016204562353755336 0.0839353723067181\n",
      "0.8571534623722302 0.5061800513050176\n",
      "0.28245160718155726 0.4027398873636385\n",
      "0.27400626856305765 0.6817617781755172\n",
      "0.5728205116755092 0.19700979757950854\n",
      "0.5283421513688321 0.9180473293392817\n",
      "0.12048127942343789 0.1130896022051403\n",
      "0.9868992796612697 0.2220828270186318\n",
      "0.6315136369424463 0.23062823135484078\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for _ in range(5):\n",
    "    i = random.choice(range(len((sub_x))))\n",
    "    linear_output = np.concatenate((random_linear(sub_x[:i]),random_linear(sub_x[i:])))\n",
    "    i2 = random.choice(range(len(linear_output)))\n",
    "    output = np.concatenate((sigmoid(linear_output[:i2]),sigmoid(linear_output[i2:])))\n",
    "    plt.plot(sub_x,output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.4593711733704513 0.1174004174914195\n",
      "0.33082058454302876 0.16451501037705352\n",
      "0.31023012945345874 0.9950431288759168\n",
      "0.3246909000590621 0.4788396746035354\n",
      "0.8617372405332395 0.7730381500543565\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for _ in range(5):\n",
    "    linear_output = random_linear(sub_x)\n",
    "    output =sigmoid(linear_output)\n",
    "    plt.plot(sub_x,output)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'VAR_MIN' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-45-a99a5f91e294>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mk\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mrandom\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrandint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mVAR_MIN\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mVAR_MAX\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mrandom\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrandint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mVAR_MIN\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mVAR_MAX\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0mmin_loss\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mfloat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'inf'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mbest_k\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mbest_b\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0mtotal_times\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1000\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'VAR_MIN' is not defined"
     ]
    }
   ],
   "source": [
    "k,b=random.randint(VAR_MIN,VAR_MAX),random.randint(VAR_MIN,VAR_MAX)\n",
    "min_loss=float('inf')\n",
    "best_k,best_b=None,None\n",
    "\n",
    "total_times=1000\n",
    "alpha=1e-4\n",
    "for t in range(total_times):\n",
    "    k1=k1+(-1)*loss对k1的偏导\n",
    "    b1=b1+(-1)*loss对b1的偏导\n",
    "    k2=k2+(-1)*loss对k2的偏导\n",
    "    b2=b2+(-1)*loss对b2的偏导\n",
    "    \n",
    "    \n",
    "    if loss_<min_loss:\n",
    "        min_loss=loss_\n",
    "        best_k, best_b=k, b\n",
    "        print('在{}时刻我找到了更好的k:{}和b:{},这个时候的loss是:{}'.format(t,k,b,loss_))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "computing_graph={\n",
    "    'k1':['L1'],\n",
    "    'k2':['L2'],\n",
    "    'x':['L1'],\n",
    "    'L2':['sigmoid'],\n",
    "    'sigmoid':[''],\n",
    "    'L2':['LOSS'],\n",
    "    'y':['LOSS']\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.7/importlib/_bootstrap.py:219: RuntimeWarning: numpy.ufunc size changed, may indicate binary incompatibility. Expected 192 from C header, got 216 from PyObject\n",
      "  return f(*args, **kwds)\n",
      "/opt/conda/lib/python3.7/importlib/_bootstrap.py:219: RuntimeWarning: numpy.ufunc size changed, may indicate binary incompatibility. Expected 192 from C header, got 216 from PyObject\n",
      "  return f(*args, **kwds)\n"
     ]
    }
   ],
   "source": [
    "import networkx as nx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_output(graph,node):\n",
    "    outputs=[]\n",
    "    for n,links in graph.items():\n",
    "        if node == n:outputs+=links\n",
    "    return outputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['L1']"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "get_output(computing_graph,'k1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
